Architected cellular piezoelectric metamaterials: Thermo-electro-mechanical properties

Abstract

Advances in additive manufacturing have recently made possible the manufacturing of smart materials with arbitrary microarchitectures, which leads to developing lightweight smart metamaterials with unprecedented multifunctional properties. In this paper, asymptotic homogenization (AH) method is developed for predicting the effective thermo-electro-mechanical properties of architected cellular piezoelectric metamaterials. The effect of pore microarchitecture (relative density and cell topology) and polarization direction on elastic, dielectric, piezoelectric, pyroelectric and thermal properties of periodic cellular piezoelectric metamaterials is explored. The pore topology is determined by Fourier series expansion. Alternative pore microarchitectures are considered by tailoring shape parameters, scaling factor, and rotation angle of the constitutive pore. Smart cellular metamaterials made of both single-phase (BaTiO3) and bi-phase (BaTiO3-expoy) piezoelectric materials are considered. Apart from effective thermo-electro-mechanical properties, a series of figures of merit for the cellular piezoelectric metamaterials, i.e. piezoelectric coupling constant, acoustic impedance, piezoelectric charge coefficient, hydrostatic figure of merit, current responsivity, voltage responsivity and pyroelectric energy harvesting figures of merit, are presented and the reason for difference between the figures of merit of different types of piezoelectric metamaterials is discussed. The figures of merit shed lights on the effect of microarchitecture on optimizing the multifunctional performance of smart cellular metamaterials for applications as structurally efficient multifunctional energy harvesters. It is found that the piezoelectric and pyroelectric figures of merit of cellular piezoelectric metamaterials can be significantly improved compared to the commonly used honeycomb cellular materials and composite materials with solid circular inclusion if an appropriate microarchitecture is selected for the pore. For example, piezoelectric charge coefficient (dh) for a transversely polarized single-phase cellular piezoelectric metamaterial with a solid volume fraction of 0.4 can be 350% higher than the corresponding figures of merit of honeycomb piezoelectric material; voltage responsivity of transversely polarized bi-phase cellular piezoelectric metamaterials with an inclusion volume fraction of 0.3 can be also 249% higher than the corresponding value of composite materials with a solid circular inclusion.